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--- advanced_tools:group_theory:group_contraction [2017/12/17 12:15]
jakobadmin [Student]
+++ advanced_tools:group_theory:group_contraction [2017/12/17 12:16]
jakobadmin [Student]
@@ Line 50: / Line 50: @@
 Both concepts are mutually the opposite. However while one can always deform to a group where we contracted from, the opposite procedure is not always possible.
+To **deform** a Lie algebra, we redefine the Lie brackets as a power series in some parameter $t$
+$$
+f_t(a,b)=[a,b]+tF_1(a,b)+t^2 F_2(a,b)+\ldots,\quad a,b\in\frak{g}\,,
+$$
+and demand that the series converges in some neighbourhood of the origin.
+----
 <blockquote>